Three dimensional (3D) capable electronics and computing hardware devices and real-time computer-generated 3D computer graphics have been a popular area of computer science for the past few decades, with innovations in visual, audio, tactile and biofeedback systems. Much of the research in this area has produced hardware and software products that are specifically designed to generate greater realism and more natural computer-human interfaces. These innovations have significantly enhanced and simplified the end-user's computing experience.
Ever since humans began to communicate through pictures, they faced a dilemma of how to accurately represent the three-dimensional world they lived in. Sculpture was used to successfully depict three-dimensional objects, but was not adequate to communicate spatial relationships between objects and within environments. To do this, early humans attempted to “flatten” what they saw around them onto two-dimensional, vertical planes (e.g. paintings, drawings, tapestries, etc.). Scenes where a person stood upright, surrounded by trees, were rendered relatively successfully on a vertical plane. But how could they represent a landscape, where the ground extended out horizontally from where the artist was standing, as far as the eye could see?
The answer is three dimensional illusions. The two dimensional pictures must provide a number of cues of the third dimension to the brain to create the illusion of three dimensional images. This effect of third dimension cues can be realistically achievable due to the fact that the brain is quite accustomed to it. The three dimensional real world is always and already converted into a two dimensional (e.g. height and width) projected image at the retina, a concave surface at the back of the eye. And from this two dimensional image, the brain, through experience and perception, generates the depth information to form the three dimensional visual image from two types of depth cues: monocular (one eye perception) and binocular (two eye perception). In general, binocular depth cues are innate and biological while monocular depth cues are learned and environmental.
Perspective drawing, together with relative size, is most often used to achieve the illusion of three dimensional depth and spatial relationships on a flat (two dimensional) surface, such as paper or canvas. Through perspective, three dimensional objects are depicted on a two dimensional plane, but “trick” the eye into appearing to be in three dimensional space. The various types of perspectives are military, cavalier, isometric, and dimetric, as shown at the top of FIG. 1.
Of special interest is the most common type of perspective, called central perspective, shown at the bottom left of FIG. 1. Central perspective, also called one-point perspective, is the simplest kind of “genuine” perspective construction, and is often taught in art and drafting classes for beginners. FIG. 2 further illustrates central perspective. Using central perspective, the chess board and chess pieces look like three dimensional objects, even though they are drawn on a two dimensional flat piece of paper. Central perspective has a central vanishing point, and rectangular objects are placed so their front sides are parallel to the picture plane. The depth of the objects is perpendicular to the picture plane. All parallel receding edges run towards a central vanishing point. The viewer looks towards this vanishing point with a straight view. When an architect or artist creates a drawing using central perspective, he must use a single-eye view. That is, the artist creating the drawing captures the image by looking through only one eye, which is perpendicular to the drawing surface.
The vast majority of images, including central perspective images, are displayed, viewed and captured in a plane perpendicular to the line of vision. Viewing the images at an angle different from 90° would result in image distortion, meaning a square would be seen as a rectangle when the viewing surface is not perpendicular to the line of vision.
Central perspective is employed extensively in 3D computer graphics, for a myriad of applications, such as scientific, data visualization, computer-generated prototyping, special effects for movies, medical imaging, and architecture, to name just a few. One of the most common and well-known 3D computing applications is 3D gaming, which is used here as an example, because the core concepts used in 3D gaming extend to all other 3D computing applications.
There is a little known class of images called “horizontal perspective” where the image appears distorted when viewing head on, but displays a three dimensional illusion when viewing from the correct viewing position. In horizontal perspective, the angle between the viewing surface and the line of vision is preferably 45°, but can be almost any angle, and the viewing surface is preferably horizontal (thus the name “horizontal perspective”), but can be any surface, as long as the line of vision forms a non-perpendicular angle to it.
Horizontal perspective images offer realistic three dimensional illusions, but are little known primarily due to the narrow viewing location (the viewer's eyepoint has to coincide precisely with the image projection eyepoint) and the complexity involved in projecting the two dimensional image or the three dimension model into the horizontal perspective image.
The generation of horizontal perspective images requires considerably more expertise to create than conventional perpendicular images. The conventional perpendicular images can be produced directly from the viewer or camera point. One need simply open one's eyes or point the camera in any direction to obtain the images. Further, with much experience in viewing three dimensional depth cues from perpendicular images, viewers can tolerate a significant amount of distortion generated by the deviations from the camera point. In contrast, the creation of a horizontal perspective image does require much manipulation. Conventional cameras, by projecting the image into the plane perpendicular to the line of sight, would not produce a horizontal perspective image. Making a horizontal drawing requires much effort and is very time consuming. Further, since humans have limited experience with horizontal perspective images, the viewer's eye must be positioned precisely where the projection eyepoint point is in order to avoid image distortion. And therefore horizontal perspective, with its difficulties, has received little attention.